3.1300 \(\int (a+b x)^{11} (c+d x)^{10} \, dx\)
Optimal. Leaf size=279 \[ \frac{10 d^9 (a+b x)^{21} (b c-a d)}{21 b^{11}}+\frac{9 d^8 (a+b x)^{20} (b c-a d)^2}{4 b^{11}}+\frac{120 d^7 (a+b x)^{19} (b c-a d)^3}{19 b^{11}}+\frac{35 d^6 (a+b x)^{18} (b c-a d)^4}{3 b^{11}}+\frac{252 d^5 (a+b x)^{17} (b c-a d)^5}{17 b^{11}}+\frac{105 d^4 (a+b x)^{16} (b c-a d)^6}{8 b^{11}}+\frac{8 d^3 (a+b x)^{15} (b c-a d)^7}{b^{11}}+\frac{45 d^2 (a+b x)^{14} (b c-a d)^8}{14 b^{11}}+\frac{10 d (a+b x)^{13} (b c-a d)^9}{13 b^{11}}+\frac{(a+b x)^{12} (b c-a d)^{10}}{12 b^{11}}+\frac{d^{10} (a+b x)^{22}}{22 b^{11}} \]
[Out]
((b*c - a*d)^10*(a + b*x)^12)/(12*b^11) + (10*d*(b*c - a*d)^9*(a + b*x)^13)/(13*b^11) + (45*d^2*(b*c - a*d)^8*
(a + b*x)^14)/(14*b^11) + (8*d^3*(b*c - a*d)^7*(a + b*x)^15)/b^11 + (105*d^4*(b*c - a*d)^6*(a + b*x)^16)/(8*b^
11) + (252*d^5*(b*c - a*d)^5*(a + b*x)^17)/(17*b^11) + (35*d^6*(b*c - a*d)^4*(a + b*x)^18)/(3*b^11) + (120*d^7
*(b*c - a*d)^3*(a + b*x)^19)/(19*b^11) + (9*d^8*(b*c - a*d)^2*(a + b*x)^20)/(4*b^11) + (10*d^9*(b*c - a*d)*(a
+ b*x)^21)/(21*b^11) + (d^10*(a + b*x)^22)/(22*b^11)
________________________________________________________________________________________
Rubi [A] time = 1.2753, antiderivative size = 279, normalized size of antiderivative = 1.,
number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used =
{43} \[ \frac{10 d^9 (a+b x)^{21} (b c-a d)}{21 b^{11}}+\frac{9 d^8 (a+b x)^{20} (b c-a d)^2}{4 b^{11}}+\frac{120 d^7 (a+b x)^{19} (b c-a d)^3}{19 b^{11}}+\frac{35 d^6 (a+b x)^{18} (b c-a d)^4}{3 b^{11}}+\frac{252 d^5 (a+b x)^{17} (b c-a d)^5}{17 b^{11}}+\frac{105 d^4 (a+b x)^{16} (b c-a d)^6}{8 b^{11}}+\frac{8 d^3 (a+b x)^{15} (b c-a d)^7}{b^{11}}+\frac{45 d^2 (a+b x)^{14} (b c-a d)^8}{14 b^{11}}+\frac{10 d (a+b x)^{13} (b c-a d)^9}{13 b^{11}}+\frac{(a+b x)^{12} (b c-a d)^{10}}{12 b^{11}}+\frac{d^{10} (a+b x)^{22}}{22 b^{11}} \]
Antiderivative was successfully verified.
[In]
Int[(a + b*x)^11*(c + d*x)^10,x]
[Out]
((b*c - a*d)^10*(a + b*x)^12)/(12*b^11) + (10*d*(b*c - a*d)^9*(a + b*x)^13)/(13*b^11) + (45*d^2*(b*c - a*d)^8*
(a + b*x)^14)/(14*b^11) + (8*d^3*(b*c - a*d)^7*(a + b*x)^15)/b^11 + (105*d^4*(b*c - a*d)^6*(a + b*x)^16)/(8*b^
11) + (252*d^5*(b*c - a*d)^5*(a + b*x)^17)/(17*b^11) + (35*d^6*(b*c - a*d)^4*(a + b*x)^18)/(3*b^11) + (120*d^7
*(b*c - a*d)^3*(a + b*x)^19)/(19*b^11) + (9*d^8*(b*c - a*d)^2*(a + b*x)^20)/(4*b^11) + (10*d^9*(b*c - a*d)*(a
+ b*x)^21)/(21*b^11) + (d^10*(a + b*x)^22)/(22*b^11)
Rule 43
Int[((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[(a + b*x)^m*(c + d
*x)^n, x], x] /; FreeQ[{a, b, c, d, n}, x] && NeQ[b*c - a*d, 0] && IGtQ[m, 0] && ( !IntegerQ[n] || (EqQ[c, 0]
&& LeQ[7*m + 4*n + 4, 0]) || LtQ[9*m + 5*(n + 1), 0] || GtQ[m + n + 2, 0])
Rubi steps
\begin{align*} \int (a+b x)^{11} (c+d x)^{10} \, dx &=\int \left (\frac{(b c-a d)^{10} (a+b x)^{11}}{b^{10}}+\frac{10 d (b c-a d)^9 (a+b x)^{12}}{b^{10}}+\frac{45 d^2 (b c-a d)^8 (a+b x)^{13}}{b^{10}}+\frac{120 d^3 (b c-a d)^7 (a+b x)^{14}}{b^{10}}+\frac{210 d^4 (b c-a d)^6 (a+b x)^{15}}{b^{10}}+\frac{252 d^5 (b c-a d)^5 (a+b x)^{16}}{b^{10}}+\frac{210 d^6 (b c-a d)^4 (a+b x)^{17}}{b^{10}}+\frac{120 d^7 (b c-a d)^3 (a+b x)^{18}}{b^{10}}+\frac{45 d^8 (b c-a d)^2 (a+b x)^{19}}{b^{10}}+\frac{10 d^9 (b c-a d) (a+b x)^{20}}{b^{10}}+\frac{d^{10} (a+b x)^{21}}{b^{10}}\right ) \, dx\\ &=\frac{(b c-a d)^{10} (a+b x)^{12}}{12 b^{11}}+\frac{10 d (b c-a d)^9 (a+b x)^{13}}{13 b^{11}}+\frac{45 d^2 (b c-a d)^8 (a+b x)^{14}}{14 b^{11}}+\frac{8 d^3 (b c-a d)^7 (a+b x)^{15}}{b^{11}}+\frac{105 d^4 (b c-a d)^6 (a+b x)^{16}}{8 b^{11}}+\frac{252 d^5 (b c-a d)^5 (a+b x)^{17}}{17 b^{11}}+\frac{35 d^6 (b c-a d)^4 (a+b x)^{18}}{3 b^{11}}+\frac{120 d^7 (b c-a d)^3 (a+b x)^{19}}{19 b^{11}}+\frac{9 d^8 (b c-a d)^2 (a+b x)^{20}}{4 b^{11}}+\frac{10 d^9 (b c-a d) (a+b x)^{21}}{21 b^{11}}+\frac{d^{10} (a+b x)^{22}}{22 b^{11}}\\ \end{align*}
Mathematica [B] time = 0.212733, size = 1702, normalized size = 6.1 \[ \frac{1}{22} b^{11} d^{10} x^{22}+\frac{1}{21} b^{10} d^9 (10 b c+11 a d) x^{21}+\frac{1}{4} b^9 d^8 \left (9 b^2 c^2+22 a b d c+11 a^2 d^2\right ) x^{20}+\frac{5}{19} b^8 d^7 \left (24 b^3 c^3+99 a b^2 d c^2+110 a^2 b d^2 c+33 a^3 d^3\right ) x^{19}+\frac{5}{6} b^7 d^6 \left (14 b^4 c^4+88 a b^3 d c^3+165 a^2 b^2 d^2 c^2+110 a^3 b d^3 c+22 a^4 d^4\right ) x^{18}+\frac{3}{17} b^6 d^5 \left (84 b^5 c^5+770 a b^4 d c^4+2200 a^2 b^3 d^2 c^3+2475 a^3 b^2 d^3 c^2+1100 a^4 b d^4 c+154 a^5 d^5\right ) x^{17}+\frac{3}{8} b^5 d^4 \left (35 b^6 c^6+462 a b^5 d c^5+1925 a^2 b^4 d^2 c^4+3300 a^3 b^3 d^3 c^3+2475 a^4 b^2 d^4 c^2+770 a^5 b d^5 c+77 a^6 d^6\right ) x^{16}+2 b^4 d^3 \left (4 b^7 c^7+77 a b^6 d c^6+462 a^2 b^5 d^2 c^5+1155 a^3 b^4 d^3 c^4+1320 a^4 b^3 d^4 c^3+693 a^5 b^2 d^5 c^2+154 a^6 b d^6 c+11 a^7 d^7\right ) x^{15}+\frac{15}{14} b^3 d^2 \left (3 b^8 c^8+88 a b^7 d c^7+770 a^2 b^6 d^2 c^6+2772 a^3 b^5 d^3 c^5+4620 a^4 b^4 d^4 c^4+3696 a^5 b^3 d^5 c^3+1386 a^6 b^2 d^6 c^2+220 a^7 b d^7 c+11 a^8 d^8\right ) x^{14}+\frac{5}{13} b^2 d \left (2 b^9 c^9+99 a b^8 d c^8+1320 a^2 b^7 d^2 c^7+6930 a^3 b^6 d^3 c^6+16632 a^4 b^5 d^4 c^5+19404 a^5 b^4 d^5 c^4+11088 a^6 b^3 d^6 c^3+2970 a^7 b^2 d^7 c^2+330 a^8 b d^8 c+11 a^9 d^9\right ) x^{13}+\frac{1}{12} b \left (b^{10} c^{10}+110 a b^9 d c^9+2475 a^2 b^8 d^2 c^8+19800 a^3 b^7 d^3 c^7+69300 a^4 b^6 d^4 c^6+116424 a^5 b^5 d^5 c^5+97020 a^6 b^4 d^6 c^4+39600 a^7 b^3 d^7 c^3+7425 a^8 b^2 d^8 c^2+550 a^9 b d^9 c+11 a^{10} d^{10}\right ) x^{12}+\frac{1}{11} a \left (11 b^{10} c^{10}+550 a b^9 d c^9+7425 a^2 b^8 d^2 c^8+39600 a^3 b^7 d^3 c^7+97020 a^4 b^6 d^4 c^6+116424 a^5 b^5 d^5 c^5+69300 a^6 b^4 d^6 c^4+19800 a^7 b^3 d^7 c^3+2475 a^8 b^2 d^8 c^2+110 a^9 b d^9 c+a^{10} d^{10}\right ) x^{11}+\frac{1}{2} a^2 c \left (11 b^9 c^9+330 a b^8 d c^8+2970 a^2 b^7 d^2 c^7+11088 a^3 b^6 d^3 c^6+19404 a^4 b^5 d^4 c^5+16632 a^5 b^4 d^5 c^4+6930 a^6 b^3 d^6 c^3+1320 a^7 b^2 d^7 c^2+99 a^8 b d^8 c+2 a^9 d^9\right ) x^{10}+\frac{5}{3} a^3 c^2 \left (11 b^8 c^8+220 a b^7 d c^7+1386 a^2 b^6 d^2 c^6+3696 a^3 b^5 d^3 c^5+4620 a^4 b^4 d^4 c^4+2772 a^5 b^3 d^5 c^3+770 a^6 b^2 d^6 c^2+88 a^7 b d^7 c+3 a^8 d^8\right ) x^9+\frac{15}{4} a^4 c^3 \left (11 b^7 c^7+154 a b^6 d c^6+693 a^2 b^5 d^2 c^5+1320 a^3 b^4 d^3 c^4+1155 a^4 b^3 d^4 c^3+462 a^5 b^2 d^5 c^2+77 a^6 b d^6 c+4 a^7 d^7\right ) x^8+\frac{6}{7} a^5 c^4 \left (77 b^6 c^6+770 a b^5 d c^5+2475 a^2 b^4 d^2 c^4+3300 a^3 b^3 d^3 c^3+1925 a^4 b^2 d^4 c^2+462 a^5 b d^5 c+35 a^6 d^6\right ) x^7+\frac{1}{2} a^6 c^5 \left (154 b^5 c^5+1100 a b^4 d c^4+2475 a^2 b^3 d^2 c^3+2200 a^3 b^2 d^3 c^2+770 a^4 b d^4 c+84 a^5 d^5\right ) x^6+3 a^7 c^6 \left (22 b^4 c^4+110 a b^3 d c^3+165 a^2 b^2 d^2 c^2+88 a^3 b d^3 c+14 a^4 d^4\right ) x^5+\frac{5}{4} a^8 c^7 \left (33 b^3 c^3+110 a b^2 d c^2+99 a^2 b d^2 c+24 a^3 d^3\right ) x^4+\frac{5}{3} a^9 c^8 \left (11 b^2 c^2+22 a b d c+9 a^2 d^2\right ) x^3+\frac{1}{2} a^{10} c^9 (11 b c+10 a d) x^2+a^{11} c^{10} x \]
Antiderivative was successfully verified.
[In]
Integrate[(a + b*x)^11*(c + d*x)^10,x]
[Out]
a^11*c^10*x + (a^10*c^9*(11*b*c + 10*a*d)*x^2)/2 + (5*a^9*c^8*(11*b^2*c^2 + 22*a*b*c*d + 9*a^2*d^2)*x^3)/3 + (
5*a^8*c^7*(33*b^3*c^3 + 110*a*b^2*c^2*d + 99*a^2*b*c*d^2 + 24*a^3*d^3)*x^4)/4 + 3*a^7*c^6*(22*b^4*c^4 + 110*a*
b^3*c^3*d + 165*a^2*b^2*c^2*d^2 + 88*a^3*b*c*d^3 + 14*a^4*d^4)*x^5 + (a^6*c^5*(154*b^5*c^5 + 1100*a*b^4*c^4*d
+ 2475*a^2*b^3*c^3*d^2 + 2200*a^3*b^2*c^2*d^3 + 770*a^4*b*c*d^4 + 84*a^5*d^5)*x^6)/2 + (6*a^5*c^4*(77*b^6*c^6
+ 770*a*b^5*c^5*d + 2475*a^2*b^4*c^4*d^2 + 3300*a^3*b^3*c^3*d^3 + 1925*a^4*b^2*c^2*d^4 + 462*a^5*b*c*d^5 + 35*
a^6*d^6)*x^7)/7 + (15*a^4*c^3*(11*b^7*c^7 + 154*a*b^6*c^6*d + 693*a^2*b^5*c^5*d^2 + 1320*a^3*b^4*c^4*d^3 + 115
5*a^4*b^3*c^3*d^4 + 462*a^5*b^2*c^2*d^5 + 77*a^6*b*c*d^6 + 4*a^7*d^7)*x^8)/4 + (5*a^3*c^2*(11*b^8*c^8 + 220*a*
b^7*c^7*d + 1386*a^2*b^6*c^6*d^2 + 3696*a^3*b^5*c^5*d^3 + 4620*a^4*b^4*c^4*d^4 + 2772*a^5*b^3*c^3*d^5 + 770*a^
6*b^2*c^2*d^6 + 88*a^7*b*c*d^7 + 3*a^8*d^8)*x^9)/3 + (a^2*c*(11*b^9*c^9 + 330*a*b^8*c^8*d + 2970*a^2*b^7*c^7*d
^2 + 11088*a^3*b^6*c^6*d^3 + 19404*a^4*b^5*c^5*d^4 + 16632*a^5*b^4*c^4*d^5 + 6930*a^6*b^3*c^3*d^6 + 1320*a^7*b
^2*c^2*d^7 + 99*a^8*b*c*d^8 + 2*a^9*d^9)*x^10)/2 + (a*(11*b^10*c^10 + 550*a*b^9*c^9*d + 7425*a^2*b^8*c^8*d^2 +
39600*a^3*b^7*c^7*d^3 + 97020*a^4*b^6*c^6*d^4 + 116424*a^5*b^5*c^5*d^5 + 69300*a^6*b^4*c^4*d^6 + 19800*a^7*b^
3*c^3*d^7 + 2475*a^8*b^2*c^2*d^8 + 110*a^9*b*c*d^9 + a^10*d^10)*x^11)/11 + (b*(b^10*c^10 + 110*a*b^9*c^9*d + 2
475*a^2*b^8*c^8*d^2 + 19800*a^3*b^7*c^7*d^3 + 69300*a^4*b^6*c^6*d^4 + 116424*a^5*b^5*c^5*d^5 + 97020*a^6*b^4*c
^4*d^6 + 39600*a^7*b^3*c^3*d^7 + 7425*a^8*b^2*c^2*d^8 + 550*a^9*b*c*d^9 + 11*a^10*d^10)*x^12)/12 + (5*b^2*d*(2
*b^9*c^9 + 99*a*b^8*c^8*d + 1320*a^2*b^7*c^7*d^2 + 6930*a^3*b^6*c^6*d^3 + 16632*a^4*b^5*c^5*d^4 + 19404*a^5*b^
4*c^4*d^5 + 11088*a^6*b^3*c^3*d^6 + 2970*a^7*b^2*c^2*d^7 + 330*a^8*b*c*d^8 + 11*a^9*d^9)*x^13)/13 + (15*b^3*d^
2*(3*b^8*c^8 + 88*a*b^7*c^7*d + 770*a^2*b^6*c^6*d^2 + 2772*a^3*b^5*c^5*d^3 + 4620*a^4*b^4*c^4*d^4 + 3696*a^5*b
^3*c^3*d^5 + 1386*a^6*b^2*c^2*d^6 + 220*a^7*b*c*d^7 + 11*a^8*d^8)*x^14)/14 + 2*b^4*d^3*(4*b^7*c^7 + 77*a*b^6*c
^6*d + 462*a^2*b^5*c^5*d^2 + 1155*a^3*b^4*c^4*d^3 + 1320*a^4*b^3*c^3*d^4 + 693*a^5*b^2*c^2*d^5 + 154*a^6*b*c*d
^6 + 11*a^7*d^7)*x^15 + (3*b^5*d^4*(35*b^6*c^6 + 462*a*b^5*c^5*d + 1925*a^2*b^4*c^4*d^2 + 3300*a^3*b^3*c^3*d^3
+ 2475*a^4*b^2*c^2*d^4 + 770*a^5*b*c*d^5 + 77*a^6*d^6)*x^16)/8 + (3*b^6*d^5*(84*b^5*c^5 + 770*a*b^4*c^4*d + 2
200*a^2*b^3*c^3*d^2 + 2475*a^3*b^2*c^2*d^3 + 1100*a^4*b*c*d^4 + 154*a^5*d^5)*x^17)/17 + (5*b^7*d^6*(14*b^4*c^4
+ 88*a*b^3*c^3*d + 165*a^2*b^2*c^2*d^2 + 110*a^3*b*c*d^3 + 22*a^4*d^4)*x^18)/6 + (5*b^8*d^7*(24*b^3*c^3 + 99*
a*b^2*c^2*d + 110*a^2*b*c*d^2 + 33*a^3*d^3)*x^19)/19 + (b^9*d^8*(9*b^2*c^2 + 22*a*b*c*d + 11*a^2*d^2)*x^20)/4
+ (b^10*d^9*(10*b*c + 11*a*d)*x^21)/21 + (b^11*d^10*x^22)/22
________________________________________________________________________________________
Maple [B] time = 0.004, size = 1741, normalized size = 6.2 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((b*x+a)^11*(d*x+c)^10,x)
[Out]
1/22*b^11*d^10*x^22+1/21*(11*a*b^10*d^10+10*b^11*c*d^9)*x^21+1/20*(55*a^2*b^9*d^10+110*a*b^10*c*d^9+45*b^11*c^
2*d^8)*x^20+1/19*(165*a^3*b^8*d^10+550*a^2*b^9*c*d^9+495*a*b^10*c^2*d^8+120*b^11*c^3*d^7)*x^19+1/18*(330*a^4*b
^7*d^10+1650*a^3*b^8*c*d^9+2475*a^2*b^9*c^2*d^8+1320*a*b^10*c^3*d^7+210*b^11*c^4*d^6)*x^18+1/17*(462*a^5*b^6*d
^10+3300*a^4*b^7*c*d^9+7425*a^3*b^8*c^2*d^8+6600*a^2*b^9*c^3*d^7+2310*a*b^10*c^4*d^6+252*b^11*c^5*d^5)*x^17+1/
16*(462*a^6*b^5*d^10+4620*a^5*b^6*c*d^9+14850*a^4*b^7*c^2*d^8+19800*a^3*b^8*c^3*d^7+11550*a^2*b^9*c^4*d^6+2772
*a*b^10*c^5*d^5+210*b^11*c^6*d^4)*x^16+1/15*(330*a^7*b^4*d^10+4620*a^6*b^5*c*d^9+20790*a^5*b^6*c^2*d^8+39600*a
^4*b^7*c^3*d^7+34650*a^3*b^8*c^4*d^6+13860*a^2*b^9*c^5*d^5+2310*a*b^10*c^6*d^4+120*b^11*c^7*d^3)*x^15+1/14*(16
5*a^8*b^3*d^10+3300*a^7*b^4*c*d^9+20790*a^6*b^5*c^2*d^8+55440*a^5*b^6*c^3*d^7+69300*a^4*b^7*c^4*d^6+41580*a^3*
b^8*c^5*d^5+11550*a^2*b^9*c^6*d^4+1320*a*b^10*c^7*d^3+45*b^11*c^8*d^2)*x^14+1/13*(55*a^9*b^2*d^10+1650*a^8*b^3
*c*d^9+14850*a^7*b^4*c^2*d^8+55440*a^6*b^5*c^3*d^7+97020*a^5*b^6*c^4*d^6+83160*a^4*b^7*c^5*d^5+34650*a^3*b^8*c
^6*d^4+6600*a^2*b^9*c^7*d^3+495*a*b^10*c^8*d^2+10*b^11*c^9*d)*x^13+1/12*(11*a^10*b*d^10+550*a^9*b^2*c*d^9+7425
*a^8*b^3*c^2*d^8+39600*a^7*b^4*c^3*d^7+97020*a^6*b^5*c^4*d^6+116424*a^5*b^6*c^5*d^5+69300*a^4*b^7*c^6*d^4+1980
0*a^3*b^8*c^7*d^3+2475*a^2*b^9*c^8*d^2+110*a*b^10*c^9*d+b^11*c^10)*x^12+1/11*(a^11*d^10+110*a^10*b*c*d^9+2475*
a^9*b^2*c^2*d^8+19800*a^8*b^3*c^3*d^7+69300*a^7*b^4*c^4*d^6+116424*a^6*b^5*c^5*d^5+97020*a^5*b^6*c^6*d^4+39600
*a^4*b^7*c^7*d^3+7425*a^3*b^8*c^8*d^2+550*a^2*b^9*c^9*d+11*a*b^10*c^10)*x^11+1/10*(10*a^11*c*d^9+495*a^10*b*c^
2*d^8+6600*a^9*b^2*c^3*d^7+34650*a^8*b^3*c^4*d^6+83160*a^7*b^4*c^5*d^5+97020*a^6*b^5*c^6*d^4+55440*a^5*b^6*c^7
*d^3+14850*a^4*b^7*c^8*d^2+1650*a^3*b^8*c^9*d+55*a^2*b^9*c^10)*x^10+1/9*(45*a^11*c^2*d^8+1320*a^10*b*c^3*d^7+1
1550*a^9*b^2*c^4*d^6+41580*a^8*b^3*c^5*d^5+69300*a^7*b^4*c^6*d^4+55440*a^6*b^5*c^7*d^3+20790*a^5*b^6*c^8*d^2+3
300*a^4*b^7*c^9*d+165*a^3*b^8*c^10)*x^9+1/8*(120*a^11*c^3*d^7+2310*a^10*b*c^4*d^6+13860*a^9*b^2*c^5*d^5+34650*
a^8*b^3*c^6*d^4+39600*a^7*b^4*c^7*d^3+20790*a^6*b^5*c^8*d^2+4620*a^5*b^6*c^9*d+330*a^4*b^7*c^10)*x^8+1/7*(210*
a^11*c^4*d^6+2772*a^10*b*c^5*d^5+11550*a^9*b^2*c^6*d^4+19800*a^8*b^3*c^7*d^3+14850*a^7*b^4*c^8*d^2+4620*a^6*b^
5*c^9*d+462*a^5*b^6*c^10)*x^7+1/6*(252*a^11*c^5*d^5+2310*a^10*b*c^6*d^4+6600*a^9*b^2*c^7*d^3+7425*a^8*b^3*c^8*
d^2+3300*a^7*b^4*c^9*d+462*a^6*b^5*c^10)*x^6+1/5*(210*a^11*c^6*d^4+1320*a^10*b*c^7*d^3+2475*a^9*b^2*c^8*d^2+16
50*a^8*b^3*c^9*d+330*a^7*b^4*c^10)*x^5+1/4*(120*a^11*c^7*d^3+495*a^10*b*c^8*d^2+550*a^9*b^2*c^9*d+165*a^8*b^3*
c^10)*x^4+1/3*(45*a^11*c^8*d^2+110*a^10*b*c^9*d+55*a^9*b^2*c^10)*x^3+1/2*(10*a^11*c^9*d+11*a^10*b*c^10)*x^2+a^
11*c^10*x
________________________________________________________________________________________
Maxima [B] time = 1.03146, size = 2349, normalized size = 8.42 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)^11*(d*x+c)^10,x, algorithm="maxima")
[Out]
1/22*b^11*d^10*x^22 + a^11*c^10*x + 1/21*(10*b^11*c*d^9 + 11*a*b^10*d^10)*x^21 + 1/4*(9*b^11*c^2*d^8 + 22*a*b^
10*c*d^9 + 11*a^2*b^9*d^10)*x^20 + 5/19*(24*b^11*c^3*d^7 + 99*a*b^10*c^2*d^8 + 110*a^2*b^9*c*d^9 + 33*a^3*b^8*
d^10)*x^19 + 5/6*(14*b^11*c^4*d^6 + 88*a*b^10*c^3*d^7 + 165*a^2*b^9*c^2*d^8 + 110*a^3*b^8*c*d^9 + 22*a^4*b^7*d
^10)*x^18 + 3/17*(84*b^11*c^5*d^5 + 770*a*b^10*c^4*d^6 + 2200*a^2*b^9*c^3*d^7 + 2475*a^3*b^8*c^2*d^8 + 1100*a^
4*b^7*c*d^9 + 154*a^5*b^6*d^10)*x^17 + 3/8*(35*b^11*c^6*d^4 + 462*a*b^10*c^5*d^5 + 1925*a^2*b^9*c^4*d^6 + 3300
*a^3*b^8*c^3*d^7 + 2475*a^4*b^7*c^2*d^8 + 770*a^5*b^6*c*d^9 + 77*a^6*b^5*d^10)*x^16 + 2*(4*b^11*c^7*d^3 + 77*a
*b^10*c^6*d^4 + 462*a^2*b^9*c^5*d^5 + 1155*a^3*b^8*c^4*d^6 + 1320*a^4*b^7*c^3*d^7 + 693*a^5*b^6*c^2*d^8 + 154*
a^6*b^5*c*d^9 + 11*a^7*b^4*d^10)*x^15 + 15/14*(3*b^11*c^8*d^2 + 88*a*b^10*c^7*d^3 + 770*a^2*b^9*c^6*d^4 + 2772
*a^3*b^8*c^5*d^5 + 4620*a^4*b^7*c^4*d^6 + 3696*a^5*b^6*c^3*d^7 + 1386*a^6*b^5*c^2*d^8 + 220*a^7*b^4*c*d^9 + 11
*a^8*b^3*d^10)*x^14 + 5/13*(2*b^11*c^9*d + 99*a*b^10*c^8*d^2 + 1320*a^2*b^9*c^7*d^3 + 6930*a^3*b^8*c^6*d^4 + 1
6632*a^4*b^7*c^5*d^5 + 19404*a^5*b^6*c^4*d^6 + 11088*a^6*b^5*c^3*d^7 + 2970*a^7*b^4*c^2*d^8 + 330*a^8*b^3*c*d^
9 + 11*a^9*b^2*d^10)*x^13 + 1/12*(b^11*c^10 + 110*a*b^10*c^9*d + 2475*a^2*b^9*c^8*d^2 + 19800*a^3*b^8*c^7*d^3
+ 69300*a^4*b^7*c^6*d^4 + 116424*a^5*b^6*c^5*d^5 + 97020*a^6*b^5*c^4*d^6 + 39600*a^7*b^4*c^3*d^7 + 7425*a^8*b^
3*c^2*d^8 + 550*a^9*b^2*c*d^9 + 11*a^10*b*d^10)*x^12 + 1/11*(11*a*b^10*c^10 + 550*a^2*b^9*c^9*d + 7425*a^3*b^8
*c^8*d^2 + 39600*a^4*b^7*c^7*d^3 + 97020*a^5*b^6*c^6*d^4 + 116424*a^6*b^5*c^5*d^5 + 69300*a^7*b^4*c^4*d^6 + 19
800*a^8*b^3*c^3*d^7 + 2475*a^9*b^2*c^2*d^8 + 110*a^10*b*c*d^9 + a^11*d^10)*x^11 + 1/2*(11*a^2*b^9*c^10 + 330*a
^3*b^8*c^9*d + 2970*a^4*b^7*c^8*d^2 + 11088*a^5*b^6*c^7*d^3 + 19404*a^6*b^5*c^6*d^4 + 16632*a^7*b^4*c^5*d^5 +
6930*a^8*b^3*c^4*d^6 + 1320*a^9*b^2*c^3*d^7 + 99*a^10*b*c^2*d^8 + 2*a^11*c*d^9)*x^10 + 5/3*(11*a^3*b^8*c^10 +
220*a^4*b^7*c^9*d + 1386*a^5*b^6*c^8*d^2 + 3696*a^6*b^5*c^7*d^3 + 4620*a^7*b^4*c^6*d^4 + 2772*a^8*b^3*c^5*d^5
+ 770*a^9*b^2*c^4*d^6 + 88*a^10*b*c^3*d^7 + 3*a^11*c^2*d^8)*x^9 + 15/4*(11*a^4*b^7*c^10 + 154*a^5*b^6*c^9*d +
693*a^6*b^5*c^8*d^2 + 1320*a^7*b^4*c^7*d^3 + 1155*a^8*b^3*c^6*d^4 + 462*a^9*b^2*c^5*d^5 + 77*a^10*b*c^4*d^6 +
4*a^11*c^3*d^7)*x^8 + 6/7*(77*a^5*b^6*c^10 + 770*a^6*b^5*c^9*d + 2475*a^7*b^4*c^8*d^2 + 3300*a^8*b^3*c^7*d^3 +
1925*a^9*b^2*c^6*d^4 + 462*a^10*b*c^5*d^5 + 35*a^11*c^4*d^6)*x^7 + 1/2*(154*a^6*b^5*c^10 + 1100*a^7*b^4*c^9*d
+ 2475*a^8*b^3*c^8*d^2 + 2200*a^9*b^2*c^7*d^3 + 770*a^10*b*c^6*d^4 + 84*a^11*c^5*d^5)*x^6 + 3*(22*a^7*b^4*c^1
0 + 110*a^8*b^3*c^9*d + 165*a^9*b^2*c^8*d^2 + 88*a^10*b*c^7*d^3 + 14*a^11*c^6*d^4)*x^5 + 5/4*(33*a^8*b^3*c^10
+ 110*a^9*b^2*c^9*d + 99*a^10*b*c^8*d^2 + 24*a^11*c^7*d^3)*x^4 + 5/3*(11*a^9*b^2*c^10 + 22*a^10*b*c^9*d + 9*a^
11*c^8*d^2)*x^3 + 1/2*(11*a^10*b*c^10 + 10*a^11*c^9*d)*x^2
________________________________________________________________________________________
Fricas [B] time = 1.73361, size = 4709, normalized size = 16.88 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)^11*(d*x+c)^10,x, algorithm="fricas")
[Out]
1/22*x^22*d^10*b^11 + 10/21*x^21*d^9*c*b^11 + 11/21*x^21*d^10*b^10*a + 9/4*x^20*d^8*c^2*b^11 + 11/2*x^20*d^9*c
*b^10*a + 11/4*x^20*d^10*b^9*a^2 + 120/19*x^19*d^7*c^3*b^11 + 495/19*x^19*d^8*c^2*b^10*a + 550/19*x^19*d^9*c*b
^9*a^2 + 165/19*x^19*d^10*b^8*a^3 + 35/3*x^18*d^6*c^4*b^11 + 220/3*x^18*d^7*c^3*b^10*a + 275/2*x^18*d^8*c^2*b^
9*a^2 + 275/3*x^18*d^9*c*b^8*a^3 + 55/3*x^18*d^10*b^7*a^4 + 252/17*x^17*d^5*c^5*b^11 + 2310/17*x^17*d^6*c^4*b^
10*a + 6600/17*x^17*d^7*c^3*b^9*a^2 + 7425/17*x^17*d^8*c^2*b^8*a^3 + 3300/17*x^17*d^9*c*b^7*a^4 + 462/17*x^17*
d^10*b^6*a^5 + 105/8*x^16*d^4*c^6*b^11 + 693/4*x^16*d^5*c^5*b^10*a + 5775/8*x^16*d^6*c^4*b^9*a^2 + 2475/2*x^16
*d^7*c^3*b^8*a^3 + 7425/8*x^16*d^8*c^2*b^7*a^4 + 1155/4*x^16*d^9*c*b^6*a^5 + 231/8*x^16*d^10*b^5*a^6 + 8*x^15*
d^3*c^7*b^11 + 154*x^15*d^4*c^6*b^10*a + 924*x^15*d^5*c^5*b^9*a^2 + 2310*x^15*d^6*c^4*b^8*a^3 + 2640*x^15*d^7*
c^3*b^7*a^4 + 1386*x^15*d^8*c^2*b^6*a^5 + 308*x^15*d^9*c*b^5*a^6 + 22*x^15*d^10*b^4*a^7 + 45/14*x^14*d^2*c^8*b
^11 + 660/7*x^14*d^3*c^7*b^10*a + 825*x^14*d^4*c^6*b^9*a^2 + 2970*x^14*d^5*c^5*b^8*a^3 + 4950*x^14*d^6*c^4*b^7
*a^4 + 3960*x^14*d^7*c^3*b^6*a^5 + 1485*x^14*d^8*c^2*b^5*a^6 + 1650/7*x^14*d^9*c*b^4*a^7 + 165/14*x^14*d^10*b^
3*a^8 + 10/13*x^13*d*c^9*b^11 + 495/13*x^13*d^2*c^8*b^10*a + 6600/13*x^13*d^3*c^7*b^9*a^2 + 34650/13*x^13*d^4*
c^6*b^8*a^3 + 83160/13*x^13*d^5*c^5*b^7*a^4 + 97020/13*x^13*d^6*c^4*b^6*a^5 + 55440/13*x^13*d^7*c^3*b^5*a^6 +
14850/13*x^13*d^8*c^2*b^4*a^7 + 1650/13*x^13*d^9*c*b^3*a^8 + 55/13*x^13*d^10*b^2*a^9 + 1/12*x^12*c^10*b^11 + 5
5/6*x^12*d*c^9*b^10*a + 825/4*x^12*d^2*c^8*b^9*a^2 + 1650*x^12*d^3*c^7*b^8*a^3 + 5775*x^12*d^4*c^6*b^7*a^4 + 9
702*x^12*d^5*c^5*b^6*a^5 + 8085*x^12*d^6*c^4*b^5*a^6 + 3300*x^12*d^7*c^3*b^4*a^7 + 2475/4*x^12*d^8*c^2*b^3*a^8
+ 275/6*x^12*d^9*c*b^2*a^9 + 11/12*x^12*d^10*b*a^10 + x^11*c^10*b^10*a + 50*x^11*d*c^9*b^9*a^2 + 675*x^11*d^2
*c^8*b^8*a^3 + 3600*x^11*d^3*c^7*b^7*a^4 + 8820*x^11*d^4*c^6*b^6*a^5 + 10584*x^11*d^5*c^5*b^5*a^6 + 6300*x^11*
d^6*c^4*b^4*a^7 + 1800*x^11*d^7*c^3*b^3*a^8 + 225*x^11*d^8*c^2*b^2*a^9 + 10*x^11*d^9*c*b*a^10 + 1/11*x^11*d^10
*a^11 + 11/2*x^10*c^10*b^9*a^2 + 165*x^10*d*c^9*b^8*a^3 + 1485*x^10*d^2*c^8*b^7*a^4 + 5544*x^10*d^3*c^7*b^6*a^
5 + 9702*x^10*d^4*c^6*b^5*a^6 + 8316*x^10*d^5*c^5*b^4*a^7 + 3465*x^10*d^6*c^4*b^3*a^8 + 660*x^10*d^7*c^3*b^2*a
^9 + 99/2*x^10*d^8*c^2*b*a^10 + x^10*d^9*c*a^11 + 55/3*x^9*c^10*b^8*a^3 + 1100/3*x^9*d*c^9*b^7*a^4 + 2310*x^9*
d^2*c^8*b^6*a^5 + 6160*x^9*d^3*c^7*b^5*a^6 + 7700*x^9*d^4*c^6*b^4*a^7 + 4620*x^9*d^5*c^5*b^3*a^8 + 3850/3*x^9*
d^6*c^4*b^2*a^9 + 440/3*x^9*d^7*c^3*b*a^10 + 5*x^9*d^8*c^2*a^11 + 165/4*x^8*c^10*b^7*a^4 + 1155/2*x^8*d*c^9*b^
6*a^5 + 10395/4*x^8*d^2*c^8*b^5*a^6 + 4950*x^8*d^3*c^7*b^4*a^7 + 17325/4*x^8*d^4*c^6*b^3*a^8 + 3465/2*x^8*d^5*
c^5*b^2*a^9 + 1155/4*x^8*d^6*c^4*b*a^10 + 15*x^8*d^7*c^3*a^11 + 66*x^7*c^10*b^6*a^5 + 660*x^7*d*c^9*b^5*a^6 +
14850/7*x^7*d^2*c^8*b^4*a^7 + 19800/7*x^7*d^3*c^7*b^3*a^8 + 1650*x^7*d^4*c^6*b^2*a^9 + 396*x^7*d^5*c^5*b*a^10
+ 30*x^7*d^6*c^4*a^11 + 77*x^6*c^10*b^5*a^6 + 550*x^6*d*c^9*b^4*a^7 + 2475/2*x^6*d^2*c^8*b^3*a^8 + 1100*x^6*d^
3*c^7*b^2*a^9 + 385*x^6*d^4*c^6*b*a^10 + 42*x^6*d^5*c^5*a^11 + 66*x^5*c^10*b^4*a^7 + 330*x^5*d*c^9*b^3*a^8 + 4
95*x^5*d^2*c^8*b^2*a^9 + 264*x^5*d^3*c^7*b*a^10 + 42*x^5*d^4*c^6*a^11 + 165/4*x^4*c^10*b^3*a^8 + 275/2*x^4*d*c
^9*b^2*a^9 + 495/4*x^4*d^2*c^8*b*a^10 + 30*x^4*d^3*c^7*a^11 + 55/3*x^3*c^10*b^2*a^9 + 110/3*x^3*d*c^9*b*a^10 +
15*x^3*d^2*c^8*a^11 + 11/2*x^2*c^10*b*a^10 + 5*x^2*d*c^9*a^11 + x*c^10*a^11
________________________________________________________________________________________
Sympy [B] time = 0.280701, size = 1965, normalized size = 7.04 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)**11*(d*x+c)**10,x)
[Out]
a**11*c**10*x + b**11*d**10*x**22/22 + x**21*(11*a*b**10*d**10/21 + 10*b**11*c*d**9/21) + x**20*(11*a**2*b**9*
d**10/4 + 11*a*b**10*c*d**9/2 + 9*b**11*c**2*d**8/4) + x**19*(165*a**3*b**8*d**10/19 + 550*a**2*b**9*c*d**9/19
+ 495*a*b**10*c**2*d**8/19 + 120*b**11*c**3*d**7/19) + x**18*(55*a**4*b**7*d**10/3 + 275*a**3*b**8*c*d**9/3 +
275*a**2*b**9*c**2*d**8/2 + 220*a*b**10*c**3*d**7/3 + 35*b**11*c**4*d**6/3) + x**17*(462*a**5*b**6*d**10/17 +
3300*a**4*b**7*c*d**9/17 + 7425*a**3*b**8*c**2*d**8/17 + 6600*a**2*b**9*c**3*d**7/17 + 2310*a*b**10*c**4*d**6
/17 + 252*b**11*c**5*d**5/17) + x**16*(231*a**6*b**5*d**10/8 + 1155*a**5*b**6*c*d**9/4 + 7425*a**4*b**7*c**2*d
**8/8 + 2475*a**3*b**8*c**3*d**7/2 + 5775*a**2*b**9*c**4*d**6/8 + 693*a*b**10*c**5*d**5/4 + 105*b**11*c**6*d**
4/8) + x**15*(22*a**7*b**4*d**10 + 308*a**6*b**5*c*d**9 + 1386*a**5*b**6*c**2*d**8 + 2640*a**4*b**7*c**3*d**7
+ 2310*a**3*b**8*c**4*d**6 + 924*a**2*b**9*c**5*d**5 + 154*a*b**10*c**6*d**4 + 8*b**11*c**7*d**3) + x**14*(165
*a**8*b**3*d**10/14 + 1650*a**7*b**4*c*d**9/7 + 1485*a**6*b**5*c**2*d**8 + 3960*a**5*b**6*c**3*d**7 + 4950*a**
4*b**7*c**4*d**6 + 2970*a**3*b**8*c**5*d**5 + 825*a**2*b**9*c**6*d**4 + 660*a*b**10*c**7*d**3/7 + 45*b**11*c**
8*d**2/14) + x**13*(55*a**9*b**2*d**10/13 + 1650*a**8*b**3*c*d**9/13 + 14850*a**7*b**4*c**2*d**8/13 + 55440*a*
*6*b**5*c**3*d**7/13 + 97020*a**5*b**6*c**4*d**6/13 + 83160*a**4*b**7*c**5*d**5/13 + 34650*a**3*b**8*c**6*d**4
/13 + 6600*a**2*b**9*c**7*d**3/13 + 495*a*b**10*c**8*d**2/13 + 10*b**11*c**9*d/13) + x**12*(11*a**10*b*d**10/1
2 + 275*a**9*b**2*c*d**9/6 + 2475*a**8*b**3*c**2*d**8/4 + 3300*a**7*b**4*c**3*d**7 + 8085*a**6*b**5*c**4*d**6
+ 9702*a**5*b**6*c**5*d**5 + 5775*a**4*b**7*c**6*d**4 + 1650*a**3*b**8*c**7*d**3 + 825*a**2*b**9*c**8*d**2/4 +
55*a*b**10*c**9*d/6 + b**11*c**10/12) + x**11*(a**11*d**10/11 + 10*a**10*b*c*d**9 + 225*a**9*b**2*c**2*d**8 +
1800*a**8*b**3*c**3*d**7 + 6300*a**7*b**4*c**4*d**6 + 10584*a**6*b**5*c**5*d**5 + 8820*a**5*b**6*c**6*d**4 +
3600*a**4*b**7*c**7*d**3 + 675*a**3*b**8*c**8*d**2 + 50*a**2*b**9*c**9*d + a*b**10*c**10) + x**10*(a**11*c*d**
9 + 99*a**10*b*c**2*d**8/2 + 660*a**9*b**2*c**3*d**7 + 3465*a**8*b**3*c**4*d**6 + 8316*a**7*b**4*c**5*d**5 + 9
702*a**6*b**5*c**6*d**4 + 5544*a**5*b**6*c**7*d**3 + 1485*a**4*b**7*c**8*d**2 + 165*a**3*b**8*c**9*d + 11*a**2
*b**9*c**10/2) + x**9*(5*a**11*c**2*d**8 + 440*a**10*b*c**3*d**7/3 + 3850*a**9*b**2*c**4*d**6/3 + 4620*a**8*b*
*3*c**5*d**5 + 7700*a**7*b**4*c**6*d**4 + 6160*a**6*b**5*c**7*d**3 + 2310*a**5*b**6*c**8*d**2 + 1100*a**4*b**7
*c**9*d/3 + 55*a**3*b**8*c**10/3) + x**8*(15*a**11*c**3*d**7 + 1155*a**10*b*c**4*d**6/4 + 3465*a**9*b**2*c**5*
d**5/2 + 17325*a**8*b**3*c**6*d**4/4 + 4950*a**7*b**4*c**7*d**3 + 10395*a**6*b**5*c**8*d**2/4 + 1155*a**5*b**6
*c**9*d/2 + 165*a**4*b**7*c**10/4) + x**7*(30*a**11*c**4*d**6 + 396*a**10*b*c**5*d**5 + 1650*a**9*b**2*c**6*d*
*4 + 19800*a**8*b**3*c**7*d**3/7 + 14850*a**7*b**4*c**8*d**2/7 + 660*a**6*b**5*c**9*d + 66*a**5*b**6*c**10) +
x**6*(42*a**11*c**5*d**5 + 385*a**10*b*c**6*d**4 + 1100*a**9*b**2*c**7*d**3 + 2475*a**8*b**3*c**8*d**2/2 + 550
*a**7*b**4*c**9*d + 77*a**6*b**5*c**10) + x**5*(42*a**11*c**6*d**4 + 264*a**10*b*c**7*d**3 + 495*a**9*b**2*c**
8*d**2 + 330*a**8*b**3*c**9*d + 66*a**7*b**4*c**10) + x**4*(30*a**11*c**7*d**3 + 495*a**10*b*c**8*d**2/4 + 275
*a**9*b**2*c**9*d/2 + 165*a**8*b**3*c**10/4) + x**3*(15*a**11*c**8*d**2 + 110*a**10*b*c**9*d/3 + 55*a**9*b**2*
c**10/3) + x**2*(5*a**11*c**9*d + 11*a**10*b*c**10/2)
________________________________________________________________________________________
Giac [B] time = 1.0877, size = 2714, normalized size = 9.73 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)^11*(d*x+c)^10,x, algorithm="giac")
[Out]
1/22*b^11*d^10*x^22 + 10/21*b^11*c*d^9*x^21 + 11/21*a*b^10*d^10*x^21 + 9/4*b^11*c^2*d^8*x^20 + 11/2*a*b^10*c*d
^9*x^20 + 11/4*a^2*b^9*d^10*x^20 + 120/19*b^11*c^3*d^7*x^19 + 495/19*a*b^10*c^2*d^8*x^19 + 550/19*a^2*b^9*c*d^
9*x^19 + 165/19*a^3*b^8*d^10*x^19 + 35/3*b^11*c^4*d^6*x^18 + 220/3*a*b^10*c^3*d^7*x^18 + 275/2*a^2*b^9*c^2*d^8
*x^18 + 275/3*a^3*b^8*c*d^9*x^18 + 55/3*a^4*b^7*d^10*x^18 + 252/17*b^11*c^5*d^5*x^17 + 2310/17*a*b^10*c^4*d^6*
x^17 + 6600/17*a^2*b^9*c^3*d^7*x^17 + 7425/17*a^3*b^8*c^2*d^8*x^17 + 3300/17*a^4*b^7*c*d^9*x^17 + 462/17*a^5*b
^6*d^10*x^17 + 105/8*b^11*c^6*d^4*x^16 + 693/4*a*b^10*c^5*d^5*x^16 + 5775/8*a^2*b^9*c^4*d^6*x^16 + 2475/2*a^3*
b^8*c^3*d^7*x^16 + 7425/8*a^4*b^7*c^2*d^8*x^16 + 1155/4*a^5*b^6*c*d^9*x^16 + 231/8*a^6*b^5*d^10*x^16 + 8*b^11*
c^7*d^3*x^15 + 154*a*b^10*c^6*d^4*x^15 + 924*a^2*b^9*c^5*d^5*x^15 + 2310*a^3*b^8*c^4*d^6*x^15 + 2640*a^4*b^7*c
^3*d^7*x^15 + 1386*a^5*b^6*c^2*d^8*x^15 + 308*a^6*b^5*c*d^9*x^15 + 22*a^7*b^4*d^10*x^15 + 45/14*b^11*c^8*d^2*x
^14 + 660/7*a*b^10*c^7*d^3*x^14 + 825*a^2*b^9*c^6*d^4*x^14 + 2970*a^3*b^8*c^5*d^5*x^14 + 4950*a^4*b^7*c^4*d^6*
x^14 + 3960*a^5*b^6*c^3*d^7*x^14 + 1485*a^6*b^5*c^2*d^8*x^14 + 1650/7*a^7*b^4*c*d^9*x^14 + 165/14*a^8*b^3*d^10
*x^14 + 10/13*b^11*c^9*d*x^13 + 495/13*a*b^10*c^8*d^2*x^13 + 6600/13*a^2*b^9*c^7*d^3*x^13 + 34650/13*a^3*b^8*c
^6*d^4*x^13 + 83160/13*a^4*b^7*c^5*d^5*x^13 + 97020/13*a^5*b^6*c^4*d^6*x^13 + 55440/13*a^6*b^5*c^3*d^7*x^13 +
14850/13*a^7*b^4*c^2*d^8*x^13 + 1650/13*a^8*b^3*c*d^9*x^13 + 55/13*a^9*b^2*d^10*x^13 + 1/12*b^11*c^10*x^12 + 5
5/6*a*b^10*c^9*d*x^12 + 825/4*a^2*b^9*c^8*d^2*x^12 + 1650*a^3*b^8*c^7*d^3*x^12 + 5775*a^4*b^7*c^6*d^4*x^12 + 9
702*a^5*b^6*c^5*d^5*x^12 + 8085*a^6*b^5*c^4*d^6*x^12 + 3300*a^7*b^4*c^3*d^7*x^12 + 2475/4*a^8*b^3*c^2*d^8*x^12
+ 275/6*a^9*b^2*c*d^9*x^12 + 11/12*a^10*b*d^10*x^12 + a*b^10*c^10*x^11 + 50*a^2*b^9*c^9*d*x^11 + 675*a^3*b^8*
c^8*d^2*x^11 + 3600*a^4*b^7*c^7*d^3*x^11 + 8820*a^5*b^6*c^6*d^4*x^11 + 10584*a^6*b^5*c^5*d^5*x^11 + 6300*a^7*b
^4*c^4*d^6*x^11 + 1800*a^8*b^3*c^3*d^7*x^11 + 225*a^9*b^2*c^2*d^8*x^11 + 10*a^10*b*c*d^9*x^11 + 1/11*a^11*d^10
*x^11 + 11/2*a^2*b^9*c^10*x^10 + 165*a^3*b^8*c^9*d*x^10 + 1485*a^4*b^7*c^8*d^2*x^10 + 5544*a^5*b^6*c^7*d^3*x^1
0 + 9702*a^6*b^5*c^6*d^4*x^10 + 8316*a^7*b^4*c^5*d^5*x^10 + 3465*a^8*b^3*c^4*d^6*x^10 + 660*a^9*b^2*c^3*d^7*x^
10 + 99/2*a^10*b*c^2*d^8*x^10 + a^11*c*d^9*x^10 + 55/3*a^3*b^8*c^10*x^9 + 1100/3*a^4*b^7*c^9*d*x^9 + 2310*a^5*
b^6*c^8*d^2*x^9 + 6160*a^6*b^5*c^7*d^3*x^9 + 7700*a^7*b^4*c^6*d^4*x^9 + 4620*a^8*b^3*c^5*d^5*x^9 + 3850/3*a^9*
b^2*c^4*d^6*x^9 + 440/3*a^10*b*c^3*d^7*x^9 + 5*a^11*c^2*d^8*x^9 + 165/4*a^4*b^7*c^10*x^8 + 1155/2*a^5*b^6*c^9*
d*x^8 + 10395/4*a^6*b^5*c^8*d^2*x^8 + 4950*a^7*b^4*c^7*d^3*x^8 + 17325/4*a^8*b^3*c^6*d^4*x^8 + 3465/2*a^9*b^2*
c^5*d^5*x^8 + 1155/4*a^10*b*c^4*d^6*x^8 + 15*a^11*c^3*d^7*x^8 + 66*a^5*b^6*c^10*x^7 + 660*a^6*b^5*c^9*d*x^7 +
14850/7*a^7*b^4*c^8*d^2*x^7 + 19800/7*a^8*b^3*c^7*d^3*x^7 + 1650*a^9*b^2*c^6*d^4*x^7 + 396*a^10*b*c^5*d^5*x^7
+ 30*a^11*c^4*d^6*x^7 + 77*a^6*b^5*c^10*x^6 + 550*a^7*b^4*c^9*d*x^6 + 2475/2*a^8*b^3*c^8*d^2*x^6 + 1100*a^9*b^
2*c^7*d^3*x^6 + 385*a^10*b*c^6*d^4*x^6 + 42*a^11*c^5*d^5*x^6 + 66*a^7*b^4*c^10*x^5 + 330*a^8*b^3*c^9*d*x^5 + 4
95*a^9*b^2*c^8*d^2*x^5 + 264*a^10*b*c^7*d^3*x^5 + 42*a^11*c^6*d^4*x^5 + 165/4*a^8*b^3*c^10*x^4 + 275/2*a^9*b^2
*c^9*d*x^4 + 495/4*a^10*b*c^8*d^2*x^4 + 30*a^11*c^7*d^3*x^4 + 55/3*a^9*b^2*c^10*x^3 + 110/3*a^10*b*c^9*d*x^3 +
15*a^11*c^8*d^2*x^3 + 11/2*a^10*b*c^10*x^2 + 5*a^11*c^9*d*x^2 + a^11*c^10*x